Generator-offset property: Difference between revisions
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An ''m''-GO scale can be interpreted as a scale in a rank-(''m'' + 2) [[regular temperament]], with basis p (period), g, δ<sub>1</sub>, ...,δ<sub>''m''</sub> (though the specific tuning used may be of lower rank). | An ''m''-GO scale can be interpreted as a scale in a rank-(''m'' + 2) [[regular temperament]], with basis p (period), g, δ<sub>1</sub>, ...,δ<sub>''m''</sub> (though the specific tuning used may be of lower rank). | ||
Note: On this page, non-italicized Latin variables refer to interval sizes. | Note: On this page, non-italicized Latin variables refer to interval sizes, for example step sizes. | ||
== Other definitions == | == Other definitions == | ||
* A strengthening of the generator-offset property, tentatively named the ''swung-generator-alternant property'' (SGA), states that the alternants g<sub>1</sub> and g<sub>2</sub> can be taken to always subtend the same number of scale steps, thus both representing "detemperings" of a generator of a single-period [[mos]] scale (otherwise known as a well-formed scale). All odd GO scales are SGA, and aside from odd GO scales, only xyxz satisfies this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA. | * A strengthening of the generator-offset property, tentatively named the ''swung-generator-alternant property'' (SGA), states that the alternants g<sub>1</sub> and g<sub>2</sub> can be taken to always subtend the same number of scale steps, thus both representing "detemperings" of a generator of a single-period [[mos]] scale (otherwise known as a well-formed scale). All odd GO scales are SGA, and aside from odd GO scales, only xyxz satisfies this property. The Zarlino and diasem scales above are both SGA. [[Blackdye]] is GO but not SGA. | ||